Plato asked if you could prove f(0)= 0, then gave a proof himself. You responded to that with
No, Plato meant nothing of the sort- he certainly never said anything about the function "F(x)= x- 2" because that is NOT an odd function! Further he was not talking about two different functions which is what you are doing.
A function is odd if, for all x, f(-x)= -f(x). That is not true for F(x)= x- 2: Taking x= 3, F(3)= 3- 2= 1. Taking x= -3, F(-3)= -3- 2= -5. .
What Plato was saying was- start from f(-x)= -f(x) and let x= 0.
To show that a function, f, is continuous at x= a, we would have to prove that . Here, we have a= 0 and we know that f(0)= 0 so that reduces to . We are also told that f is "right continuous at x= 0" which means (that is the limit as we approach 0 only from the positive numbers). Now you know that f(-x)= -f(x).
Thx for ur help , this was very useful .. and thxx to plato for trying to help first